Bjørhus, Morten and Stuart, Andrew M. (1997) Waveform relaxation as a dynamical system. Mathematics of Computation, 66 (219). pp. 1101-1118. ISSN 0025-5718. doi:10.1090/S0025-5718-97-00847-8. https://resolver.caltech.edu/CaltechAUTHORS:20170612-145717225
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Abstract
In this paper the properties of waveform relaxation are studied when applied to the dynamical system generated by an autonomous ordinary differential equation. In particular, the effect of the waveform relaxation on the invariant sets of the flow is analysed. Windowed waveform relaxation is studied, whereby the iterative technique is applied on successive time intervals of length T and a fixed, finite, number of iterations taken on each window. This process does not generate a dynamical system on R+ since two different applications of the waveform algorithm over different time intervals do not, in general, commute. In order to generate a dynamical system it is necessary to consider the time T map generated by the relaxation process. This is done, and C^1-closeness of the resulting map to the time T map of the underlying ordinary differential equation is established. Using this, various results from the theory of dynamical systems are applied, and the results discussed.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1997 American Mathematical Society. Received by the editor December 19, 1994 and, in revised form, October 16, 1995. The first author was supported by the Research Council of Norway. The second author was supported by the National Science Foundation and the Office for Naval Research. | |||||||||
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| Issue or Number: | 219 | |||||||||
| Classification Code: | 1991 Mathematics Subject Classification: Primary 65L05, 34C35, 65Q05 | |||||||||
| DOI: | 10.1090/S0025-5718-97-00847-8 | |||||||||
| Record Number: | CaltechAUTHORS:20170612-145717225 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170612-145717225 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 78126 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 12 Jun 2017 22:05 | |||||||||
| Last Modified: | 15 Nov 2021 17:37 |
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